What is the answer to log_{x}(243)=-5 ?

The answer to log_{x}(243)=-5 is x= 1/3

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log_{x}(243)=-5

lo g_{x} (243) = - 5

x = \frac{1}{3}

Decimal Notation

x = 0.33333 \dots

Solution steps

lo g_{x} (243) = - 5

Apply log rules

\frac{1}{lo g _{243} ( x )} = - 5

Multiply both sides by

lo g_{243} (x)

\frac{1}{lo g _{243} ( x )} lo g_{243} (x) = - 5 lo g_{243} (x)

Simplify

1 = - 5 lo g_{243} (x)

Switch sides

- 5 lo g_{243} (x) = 1

Divide both sides by

- 5

lo g_{243} (x) = - \frac{1}{5}

Apply log rules

x = \frac{1}{3}

Verify Solutions:

x = \frac{1}{3}

True

The solution is

x = \frac{1}{3}

lo g_{2} (2 x - 1) = 4

x, lo g_{3} (4 x - 1) = 3

lo g_{4} (x) + lo g_{4} (2) = 2

0 = 34.2 - 5.7 ln (x)

ln (3 t + 1) + ln (3 t - 1) = 0